The (approximate) commutation guarantee plays an important role in our analysis of
the tensor code test, and it is an interesting question whether it is truly
necessary to test it directly with the subcube commutation test; might it
not automatically follow from success in the axis-parallel lines test? An interesting contrast can be drawn to
the Magic Square
game [1]}, [2]}, [3]},
in which questions are either cells or axis-parallel lines in a \(3 \times 3\)  square grid.
This has the same question distribution as
the axis-parallel line-point test over \([3]^2\) . For the Magic Square game,
“points” measurements along the same axis-parallel “line” commute,
but points that are not axis-aligned do not commute: indeed,
for the perfect strategy, they anticommute.
